Weyl group action on weight zero Mirković-Vilonen basis and equivariant multiplicities

Muthiah, D. (2021) Weyl group action on weight zero Mirković-Vilonen basis and equivariant multiplicities. Advances in Mathematics, 385, 107793. (doi: 10.1016/j.aim.2021.107793)

Abstract

We state a conjecture about the Weyl group action coming from Geometric Satake on zero-weight spaces in terms of equivariant multiplicities of Mirković-Vilonen cycles. We prove it for small coweights in type A. In this case, using work of Braverman, Gaitsgory and Vybornov, we show that the Mirković-Vilonen basis agrees with the Springer basis. We rephrase this in terms of equivariant multiplicities using work of Joseph and Hotta. We also have analogous results for Ginzburg’s Lagrangian construction of sln representations.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Muthiah, Dr Dinakar
• Authors: Muthiah, D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Advances in Mathematics
• Publisher: Elsevier
• ISSN: 0001-8708
• ISSN (Online): 1090-2082
• Published Online: 18 May 2021
• Copyright Holders: Copyright © 2021 Elsevier Inc.
• First Published: First published in Advances in Mathematics 385: 107793
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

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